Ergodic stationary distribution of a stochastic nonlinear epidemic model with relapse and cure. Issue 7 (3rd May 2022)

• Record Type: Journal Article
• Authors: Wang, Li-li; Huang, Nan-jing
• Is Part Of: Applicable analysis. Volume 101:Issue 7(2022)
• Page Start: 2652
• Page End: 2668
• Publication Date: 2022-05-03
• Subjects: M. Fang; Stochastic epidemic model -- nonlinear incidence rate -- relapse -- stationary distribution; 34F05 -- 60H10 -- 92D30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1817400
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we consider a stochastic general epidemic model with relapse, graded cure and nonlinear incidence rate. We show the existence and uniqueness of a global positive solution for the model under some mild conditions. We also give some sufficient conditions for ensuring the existence of an ergodic stationary distribution for the model. Moreover, we analyse the extinction of the disease described by the model. Finally, we provide some numerical simulations to illustrate our main results.